<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
<title></title>
<!--Generated on Tue Jun  3 20:04:06 2014 by LaTeXML (version 0.7.999_04) http://dlmf.nist.gov/LaTeXML/.-->

<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<link rel="stylesheet" href="../../../../../../LaTeXML.css" type="text/css">
<link rel="stylesheet" href="../../../../../../ltx-article.css" type="text/css">
<link rel="stylesheet" href="../../../../../../customRules.css" type="text/css">
</head>
<body>
<div class="ltx_page_main">
<div class="ltx_page_content">
<div class="ltx_document">
<div id="Sx1" class="ltx_section">
<h1 class="ltx_title ltx_title_section">Z-stage scanning</h1>

<div id="Sx1.p1" class="ltx_para">
<p class="ltx_p">To extend the axial field of view in 3D SMLM experiments, data can
be acquired in multiple z-stage positions <cite class="ltx_cite">[<a href="#bib.bib13" title="Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution" class="ltx_ref">1</a>]</cite>. However,
the <a href="../estimators/ui/EllipticGaussianEstimatorUI.html" title="" class="ltx_ref">astigmatism method</a>
can estimate only the relative axial positions of molecules with respect
to the focal plane. To find the absolute <img id="Sx1.p1.m1" class="ltx_Math" style="vertical-align:-2px" src="mi/mi19.png" width="13" height="12" alt="z"> coordinates, the correct
offset must be added to the axial positions of each molecule. The
new <img id="Sx1.p1.m2" class="ltx_Math" style="vertical-align:-2px" src="mi/mi19.png" width="13" height="12" alt="z"> coordinate can be determined as</p>
<table id="Sx1.Ex1" class="ltx_equation">

<tr class="ltx_equation ltx_align_baseline">
<td class="ltx_eqn_pad"></td>
<td class="ltx_align_center"><img id="Sx1.Ex1.m1" class="ltx_Math" style="vertical-align:-19px" src="mi/mi15.png" width="356" height="46" alt="z_{\mathrm{abs}}=z_{0}+z_{\mathrm{rel}}+z_{\mathrm{step}}\left(\left\lfloor%
\frac{f-1}{n_{\mathrm{im}}}\right\rfloor\bmod n_{\mathrm{pos}}\right)\,,"></td>
<td class="ltx_eqn_pad"></td>
</tr>
</table>
<p class="ltx_p">where <img id="Sx1.p1.m3" class="ltx_Math" style="vertical-align:-5px" src="mi/mi20.png" width="20" height="14" alt="z_{0}"> is the initial z-stage offset, <img id="Sx1.p1.m4" class="ltx_Math" style="vertical-align:-5px" src="mi/mi22.png" width="29" height="14" alt="z_{\mathrm{rel}}">
is the estimated molecular position relative to the focal plane (<img id="Sx1.p1.m5" class="ltx_Math" style="vertical-align:-5px" src="mi/mi21.png" width="61" height="18" alt="z_{\mathrm{rel}}=0">
for 2D data), <img id="Sx1.p1.m6" class="ltx_Math" style="vertical-align:-7px" src="mi/mi23.png" width="38" height="17" alt="z_{\mathrm{step}}"> is the step between two positions
of the Z-stage, <img id="Sx1.p1.m7" class="ltx_Math" style="vertical-align:-5px" src="mi/mi16.png" width="15" height="19" alt="f"> is the image frame in which a given molecule
appeared, <img id="Sx1.p1.m8" class="ltx_Math" style="vertical-align:-5px" src="mi/mi17.png" width="31" height="14" alt="n_{\mathrm{im}}"> is the number of images taken in each
z-stage position, and <img id="Sx1.p1.m9" class="ltx_Math" style="vertical-align:-7px" src="mi/mi18.png" width="36" height="17" alt="n_{\mathrm{pos}}"> is the number of z-stage
positions. All <img id="Sx1.p1.m10" class="ltx_Math" style="vertical-align:-2px" src="mi/mi19.png" width="13" height="12" alt="z"> variables are in nm.</p>
</div>
<div id="Sx1.SSx1" class="ltx_subsection">
<h2 class="ltx_title ltx_title_subsection">See also</h2>

<div id="Sx1.SSx1.p1" class="ltx_para">
<ul id="I1" class="ltx_itemize">
<li id="I1.i1" class="ltx_item" style="list-style-type:none;">
<span class="ltx_tag ltx_tag_itemize">•</span> 
<div id="I1.i1.p1" class="ltx_para">
<p class="ltx_p"><a href="Postprocessing.html" title="" class="ltx_ref">Post-processing analysis</a></p>
</div>
</li>
</ul>
</div>
</div>
</div>
<div id="bib" class="ltx_bibliography">
<h1 class="ltx_title ltx_title_bibliography">References</h1>

<ul id="L1" class="ltx_biblist">
<li id="bib.bib13" class="ltx_bibitem ltx_bib_article">
<span class="ltx_bibtag ltx_bib_key ltx_role_refnum">[1]</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_author">B. Huang, S. A. Jones, B. Brandenburg and X. Zhuang</span><span class="ltx_text ltx_bib_year">(2008)</span>
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_title">Whole-cell 3D STORM reveals interactions between cellular structures with nanometer-scale resolution</span>,
</span>
<span class="ltx_bibblock"><span class="ltx_text ltx_bib_journal">Nature Methods</span> <span class="ltx_text ltx_bib_volume">5</span> (<span class="ltx_text ltx_bib_number">12</span>), <span class="ltx_text ltx_bib_pages"> pp. 1047–52</span>.
</span>
<span class="ltx_bibblock">External Links: <span class="ltx_text ltx_bib_links"><a href="http://dx.doi.org/10.1038/nmeth.1274" title="" class="ltx_ref doi ltx_bib_external">Document</a></span>.
</span>
<span class="ltx_bibblock ltx_bib_cited">Cited by: <a href="#Sx1.p1" title="Z-stage scanning" class="ltx_ref"><span class="ltx_text ltx_ref_title">Z-stage scanning</span></a>.
</span>
</li>
</ul>
</div>
</div>
</div>
<div class="ltx_page_footer">
<div class="ltx_page_logo">Generated  on Tue Jun  3 20:04:06 2014 by <a href="http://dlmf.nist.gov/LaTeXML/">LaTeXML <img src="" alt="[LOGO]"></a>
</div>
</div>
</div>
</body>
</html>
